Optimal. Leaf size=443 \[ 3 \text{PolyLog}\left (2,-\frac{2 x}{1+\sqrt{5}}\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \text{PolyLog}\left (2,-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \text{PolyLog}\left (2,\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right )-3 \text{PolyLog}\left (2,\frac{2 x}{1-\sqrt{5}}+1\right )-\frac{\log ^2\left (x^2+x-1\right )}{2 x^2}+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (x^2+x-1\right ) \log \left (2 x-\sqrt{5}+1\right )-3 \log (x) \log \left (x^2+x-1\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (2 x+\sqrt{5}+1\right ) \log \left (x^2+x-1\right )+\frac{\log \left (x^2+x-1\right )}{x}-\frac{1}{4} \left (3+\sqrt{5}\right ) \log ^2\left (2 x-\sqrt{5}+1\right )-\frac{1}{4} \left (3-\sqrt{5}\right ) \log ^2\left (2 x+\sqrt{5}+1\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (2 x-\sqrt{5}+1\right )+3 \log \left (\frac{1}{2} \left (\sqrt{5}-1\right )\right ) \log \left (2 x-\sqrt{5}+1\right )-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (2 x-\sqrt{5}+1\right )+\log (x)-\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (2 x+\sqrt{5}+1\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (2 x+\sqrt{5}+1\right )+3 \log (x) \log \left (\frac{2 x}{1+\sqrt{5}}+1\right ) \]
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Rubi [A] time = 0.683829, antiderivative size = 443, normalized size of antiderivative = 1., number of steps used = 34, number of rules used = 16, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1.231, Rules used = {2525, 2528, 800, 632, 31, 2524, 2357, 2316, 2315, 2317, 2391, 2418, 2390, 2301, 2394, 2393} \[ 3 \text{PolyLog}\left (2,-\frac{2 x}{1+\sqrt{5}}\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \text{PolyLog}\left (2,-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \text{PolyLog}\left (2,\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right )-3 \text{PolyLog}\left (2,\frac{2 x}{1-\sqrt{5}}+1\right )-\frac{\log ^2\left (x^2+x-1\right )}{2 x^2}+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (x^2+x-1\right ) \log \left (2 x-\sqrt{5}+1\right )-3 \log (x) \log \left (x^2+x-1\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (2 x+\sqrt{5}+1\right ) \log \left (x^2+x-1\right )+\frac{\log \left (x^2+x-1\right )}{x}-\frac{1}{4} \left (3+\sqrt{5}\right ) \log ^2\left (2 x-\sqrt{5}+1\right )-\frac{1}{4} \left (3-\sqrt{5}\right ) \log ^2\left (2 x+\sqrt{5}+1\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (2 x-\sqrt{5}+1\right )+3 \log \left (\frac{1}{2} \left (\sqrt{5}-1\right )\right ) \log \left (2 x-\sqrt{5}+1\right )-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (2 x-\sqrt{5}+1\right )+\log (x)-\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (-\frac{2 x-\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (2 x+\sqrt{5}+1\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (2 x+\sqrt{5}+1\right )+3 \log (x) \log \left (\frac{2 x}{1+\sqrt{5}}+1\right ) \]
Antiderivative was successfully verified.
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Rule 2525
Rule 2528
Rule 800
Rule 632
Rule 31
Rule 2524
Rule 2357
Rule 2316
Rule 2315
Rule 2317
Rule 2391
Rule 2418
Rule 2390
Rule 2301
Rule 2394
Rule 2393
Rubi steps
\begin{align*} \int \frac{\log ^2\left (-1+x+x^2\right )}{x^3} \, dx &=-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+\int \frac{(1+2 x) \log \left (-1+x+x^2\right )}{x^2 \left (-1+x+x^2\right )} \, dx\\ &=-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+\int \left (-\frac{\log \left (-1+x+x^2\right )}{x^2}-\frac{3 \log \left (-1+x+x^2\right )}{x}+\frac{(4+3 x) \log \left (-1+x+x^2\right )}{-1+x+x^2}\right ) \, dx\\ &=-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}-3 \int \frac{\log \left (-1+x+x^2\right )}{x} \, dx-\int \frac{\log \left (-1+x+x^2\right )}{x^2} \, dx+\int \frac{(4+3 x) \log \left (-1+x+x^2\right )}{-1+x+x^2} \, dx\\ &=\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \int \frac{(1+2 x) \log (x)}{-1+x+x^2} \, dx-\int \frac{1+2 x}{x \left (-1+x+x^2\right )} \, dx+\int \left (\frac{\left (3+\sqrt{5}\right ) \log \left (-1+x+x^2\right )}{1-\sqrt{5}+2 x}+\frac{\left (3-\sqrt{5}\right ) \log \left (-1+x+x^2\right )}{1+\sqrt{5}+2 x}\right ) \, dx\\ &=\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \int \left (\frac{2 \log (x)}{1-\sqrt{5}+2 x}+\frac{2 \log (x)}{1+\sqrt{5}+2 x}\right ) \, dx+\left (3-\sqrt{5}\right ) \int \frac{\log \left (-1+x+x^2\right )}{1+\sqrt{5}+2 x} \, dx+\left (3+\sqrt{5}\right ) \int \frac{\log \left (-1+x+x^2\right )}{1-\sqrt{5}+2 x} \, dx-\int \left (-\frac{1}{x}+\frac{3+x}{-1+x+x^2}\right ) \, dx\\ &=\log (x)+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+6 \int \frac{\log (x)}{1-\sqrt{5}+2 x} \, dx+6 \int \frac{\log (x)}{1+\sqrt{5}+2 x} \, dx+\frac{1}{2} \left (-3-\sqrt{5}\right ) \int \frac{(1+2 x) \log \left (1-\sqrt{5}+2 x\right )}{-1+x+x^2} \, dx+\frac{1}{2} \left (-3+\sqrt{5}\right ) \int \frac{(1+2 x) \log \left (1+\sqrt{5}+2 x\right )}{-1+x+x^2} \, dx-\int \frac{3+x}{-1+x+x^2} \, dx\\ &=\log (x)+3 \log \left (\frac{1}{2} \left (-1+\sqrt{5}\right )\right ) \log \left (1-\sqrt{5}+2 x\right )+3 \log (x) \log \left (1+\frac{2 x}{1+\sqrt{5}}\right )+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}-3 \int \frac{\log \left (1+\frac{2 x}{1+\sqrt{5}}\right )}{x} \, dx+6 \int \frac{\log \left (-\frac{2 x}{1-\sqrt{5}}\right )}{1-\sqrt{5}+2 x} \, dx+\frac{1}{2} \left (-3-\sqrt{5}\right ) \int \left (\frac{2 \log \left (1-\sqrt{5}+2 x\right )}{1-\sqrt{5}+2 x}+\frac{2 \log \left (1-\sqrt{5}+2 x\right )}{1+\sqrt{5}+2 x}\right ) \, dx+\frac{1}{2} \left (-3+\sqrt{5}\right ) \int \left (\frac{2 \log \left (1+\sqrt{5}+2 x\right )}{1-\sqrt{5}+2 x}+\frac{2 \log \left (1+\sqrt{5}+2 x\right )}{1+\sqrt{5}+2 x}\right ) \, dx+\frac{1}{2} \left (-1+\sqrt{5}\right ) \int \frac{1}{\frac{1}{2}+\frac{\sqrt{5}}{2}+x} \, dx-\frac{1}{2} \left (1+\sqrt{5}\right ) \int \frac{1}{\frac{1}{2}-\frac{\sqrt{5}}{2}+x} \, dx\\ &=\log (x)-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right )+3 \log \left (\frac{1}{2} \left (-1+\sqrt{5}\right )\right ) \log \left (1-\sqrt{5}+2 x\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right )+3 \log (x) \log \left (1+\frac{2 x}{1+\sqrt{5}}\right )+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \text{Li}_2\left (-\frac{2 x}{1+\sqrt{5}}\right )-3 \text{Li}_2\left (1+\frac{2 x}{1-\sqrt{5}}\right )+\left (-3-\sqrt{5}\right ) \int \frac{\log \left (1-\sqrt{5}+2 x\right )}{1-\sqrt{5}+2 x} \, dx+\left (-3-\sqrt{5}\right ) \int \frac{\log \left (1-\sqrt{5}+2 x\right )}{1+\sqrt{5}+2 x} \, dx+\left (-3+\sqrt{5}\right ) \int \frac{\log \left (1+\sqrt{5}+2 x\right )}{1-\sqrt{5}+2 x} \, dx+\left (-3+\sqrt{5}\right ) \int \frac{\log \left (1+\sqrt{5}+2 x\right )}{1+\sqrt{5}+2 x} \, dx\\ &=\log (x)-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right )+3 \log \left (\frac{1}{2} \left (-1+\sqrt{5}\right )\right ) \log \left (1-\sqrt{5}+2 x\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (-\frac{1-\sqrt{5}+2 x}{2 \sqrt{5}}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (\frac{1+\sqrt{5}+2 x}{2 \sqrt{5}}\right )+3 \log (x) \log \left (1+\frac{2 x}{1+\sqrt{5}}\right )+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \text{Li}_2\left (-\frac{2 x}{1+\sqrt{5}}\right )-3 \text{Li}_2\left (1+\frac{2 x}{1-\sqrt{5}}\right )+\frac{1}{2} \left (-3-\sqrt{5}\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,1-\sqrt{5}+2 x\right )+\left (3-\sqrt{5}\right ) \int \frac{\log \left (\frac{2 \left (1-\sqrt{5}+2 x\right )}{2 \left (1-\sqrt{5}\right )-2 \left (1+\sqrt{5}\right )}\right )}{1+\sqrt{5}+2 x} \, dx+\frac{1}{2} \left (-3+\sqrt{5}\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,1+\sqrt{5}+2 x\right )+\left (3+\sqrt{5}\right ) \int \frac{\log \left (\frac{2 \left (1+\sqrt{5}+2 x\right )}{-2 \left (1-\sqrt{5}\right )+2 \left (1+\sqrt{5}\right )}\right )}{1-\sqrt{5}+2 x} \, dx\\ &=\log (x)-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right )+3 \log \left (\frac{1}{2} \left (-1+\sqrt{5}\right )\right ) \log \left (1-\sqrt{5}+2 x\right )-\frac{1}{4} \left (3+\sqrt{5}\right ) \log ^2\left (1-\sqrt{5}+2 x\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (-\frac{1-\sqrt{5}+2 x}{2 \sqrt{5}}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{4} \left (3-\sqrt{5}\right ) \log ^2\left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (\frac{1+\sqrt{5}+2 x}{2 \sqrt{5}}\right )+3 \log (x) \log \left (1+\frac{2 x}{1+\sqrt{5}}\right )+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \text{Li}_2\left (-\frac{2 x}{1+\sqrt{5}}\right )-3 \text{Li}_2\left (1+\frac{2 x}{1-\sqrt{5}}\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{2 x}{2 \left (1-\sqrt{5}\right )-2 \left (1+\sqrt{5}\right )}\right )}{x} \, dx,x,1+\sqrt{5}+2 x\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{2 x}{-2 \left (1-\sqrt{5}\right )+2 \left (1+\sqrt{5}\right )}\right )}{x} \, dx,x,1-\sqrt{5}+2 x\right )\\ &=\log (x)-\frac{1}{2} \left (1+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right )+3 \log \left (\frac{1}{2} \left (-1+\sqrt{5}\right )\right ) \log \left (1-\sqrt{5}+2 x\right )-\frac{1}{4} \left (3+\sqrt{5}\right ) \log ^2\left (1-\sqrt{5}+2 x\right )-\frac{1}{2} \left (1-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (-\frac{1-\sqrt{5}+2 x}{2 \sqrt{5}}\right ) \log \left (1+\sqrt{5}+2 x\right )-\frac{1}{4} \left (3-\sqrt{5}\right ) \log ^2\left (1+\sqrt{5}+2 x\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (\frac{1+\sqrt{5}+2 x}{2 \sqrt{5}}\right )+3 \log (x) \log \left (1+\frac{2 x}{1+\sqrt{5}}\right )+\frac{\log \left (-1+x+x^2\right )}{x}-3 \log (x) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3+\sqrt{5}\right ) \log \left (1-\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )+\frac{1}{2} \left (3-\sqrt{5}\right ) \log \left (1+\sqrt{5}+2 x\right ) \log \left (-1+x+x^2\right )-\frac{\log ^2\left (-1+x+x^2\right )}{2 x^2}+3 \text{Li}_2\left (-\frac{2 x}{1+\sqrt{5}}\right )-\frac{1}{2} \left (3+\sqrt{5}\right ) \text{Li}_2\left (-\frac{1-\sqrt{5}+2 x}{2 \sqrt{5}}\right )-\frac{1}{2} \left (3-\sqrt{5}\right ) \text{Li}_2\left (\frac{1+\sqrt{5}+2 x}{2 \sqrt{5}}\right )-3 \text{Li}_2\left (1+\frac{2 x}{1-\sqrt{5}}\right )\\ \end{align*}
Mathematica [A] time = 0.74486, size = 826, normalized size = 1.86 \[ \frac{x \left (\sqrt{5} x \log ^2\left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )+3 x \log ^2\left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-2 \sqrt{5} x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-6 x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )+12 x \log (x) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-12 x \log \left (\frac{2 x}{-1+\sqrt{5}}\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )+2 \sqrt{5} x \log \left (2 x+\sqrt{5}+1\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-6 x \log \left (2 x+\sqrt{5}+1\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-2 \sqrt{5} x \log \left (\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )+6 x \log \left (\frac{2 x+\sqrt{5}+1}{2 \sqrt{5}}\right ) \log \left (x-\frac{\sqrt{5}}{2}+\frac{1}{2}\right )-\sqrt{5} x \log ^2\left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right )+3 x \log ^2\left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right )+4 x \log (x)-12 x \log \left (\frac{1}{2} \left (1+\sqrt{5}\right )\right ) \log (x)-2 \sqrt{5} x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right )-6 x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right )+12 x \log (x) \log \left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right )-2 \sqrt{5} x \log \left (2 x-\sqrt{5}+1\right )-2 x \log \left (2 x-\sqrt{5}+1\right )+\sqrt{5} x \log (5) \log \left (2 x-\sqrt{5}+1\right )+3 x \log (5) \log \left (2 x-\sqrt{5}+1\right )+2 \sqrt{5} x \log \left (2 x+\sqrt{5}+1\right )-2 x \log \left (2 x+\sqrt{5}+1\right )+2 \sqrt{5} x \log \left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right ) \log \left (2 x+\sqrt{5}+1\right )-6 x \log \left (x+\frac{1}{2} \left (1+\sqrt{5}\right )\right ) \log \left (2 x+\sqrt{5}+1\right )+2 \sqrt{5} x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x^2+x-1\right )+6 x \log \left (-2 x+\sqrt{5}-1\right ) \log \left (x^2+x-1\right )-12 x \log (x) \log \left (x^2+x-1\right )-2 \sqrt{5} x \log \left (2 x+\sqrt{5}+1\right ) \log \left (x^2+x-1\right )+6 x \log \left (2 x+\sqrt{5}+1\right ) \log \left (x^2+x-1\right )+4 \log \left (x^2+x-1\right )-4 \sqrt{5} x \text{PolyLog}\left (2,\frac{-2 x+\sqrt{5}-1}{2 \sqrt{5}}\right )-12 x \text{PolyLog}\left (2,\frac{-2 x+\sqrt{5}-1}{-1+\sqrt{5}}\right )+12 x \text{PolyLog}\left (2,-\frac{2 x}{1+\sqrt{5}}\right )\right )-2 \log ^2\left (x^2+x-1\right )}{4 x^2} \]
Warning: Unable to verify antiderivative.
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Maple [F] time = 0.022, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ({x}^{2}+x-1 \right ) \right ) ^{2}}{{x}^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{\log \left (x^{2} + x - 1\right )^{2}}{2 \, x^{2}} + \int \frac{{\left (2 \, x + 1\right )} \log \left (x^{2} + x - 1\right )}{x^{4} + x^{3} - x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (x^{2} + x - 1\right )^{2}}{x^{3}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (x^{2} + x - 1\right )^{2}}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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